Within the last few years, there has been a move towards using statistical models in conjunction with neural networks with the end goal of being able to better answer the question, "what do our models know?". From this trend, classical metrics such as Prediction Interval Coverage Probability (PICP) and new metrics such as calibration error have entered the general repertoire of model evaluation in order to gain better insight into how the uncertainty of our model compares to reality. One important component of uncertainty modeling is model uncertainty (epistemic uncertainty), a measurement of what the model does and does not know. However, current evaluation techniques tends to conflate model uncertainty with aleatoric uncertainty (irreducible error), leading to incorrect conclusions. In this paper, using posterior predictive checks, we show how calibration error and its variants are almost always incorrect to use given model uncertainty, and further show how this mistake can lead to trust in bad models and mistrust in good models. Though posterior predictive checks has often been used for in-sample evaluation of Bayesian models, we show it still has an important place in the modern deep learning world.

Learning the structure of a Bayesian Network (BN) with score-based solutions involves exploring the search space of possible graphs and moving towards the graph that maximises a given objective function. Some algorithms offer exact solutions that guarantee to return the graph with the highest objective score, while others offer approximate solutions in exchange for reduced computational complexity. This paper describes an approximate BN structure learning algorithm, which we call Model Averaging Hill-Climbing (MAHC), that combines two novel strategies with hill-climbing search. The algorithm starts by pruning the search space of graphs, where the pruning strategy can be viewed as an aggressive version of the pruning strategies that are typically applied to combinatorial optimisation structure learning problems. It then performs model averaging in the hill-climbing search process and moves to the neighbouring graph that maximises the objective function, on average, for that neighbouring graph and over all its valid neighbouring graphs. Comparisons with other algorithms spanning different classes of learning suggest that the combination of aggressive pruning with model averaging is both effective and efficient, particularly in the presence of data noise.

Autonomous Land Vehicles (ALV) shall efficiently recognize the ground in unknown environments. A novel $\mathcal{GP}$-based method is proposed for the ground segmentation task in rough driving scenarios. A non-stationary covariance function is utilized as the kernel for the $\mathcal{GP}$. The ground surface behavior is assumed to only demonstrate local-smoothness. Thus, point estimates of the kernel's length-scales are obtained. Thus, two Gaussian processes are introduced to separately model the observation and local characteristics of the data. While, the \textit{observation process} is used to model the ground, the \textit{latent process} is put on length-scale values to estimate point values of length-scales at each input location. Input locations for this latent process are chosen in a physically-motivated procedure to represent an intuition about ground condition. Furthermore, an intuitive guess of length-scale value is represented by assuming the existence of hypothetical surfaces in the environment that every bunch of data points may be assumed to be resulted from measurements from this surfaces. Bayesian inference is implemented using \textit{maximum a Posteriori} criterion. The log-marginal likelihood function is assumed to be a multi-task objective function, to represent a whole-frame unbiased view of the ground at each frame. Simulation results shows the effectiveness of the proposed method even in an uneven, rough scene which outperforms similar Gaussian process based ground segmentation methods. While adjacent segments do not have similar ground structure in an uneven scene, the proposed method gives an efficient ground estimation based on a whole-frame viewpoint instead of just estimating segment-wise probable ground surfaces.

This study is inspired by those of Huang et al. (Soft Comput. 25, 2513--2520, 2021) and Wang et al. (Inf. Sci. 179, 3026--3040, 2009) in which some ranking techniques for interval-valued intuitionistic fuzzy numbers (IVIFNs) were introduced. In this study, we prove that the space of all IVIFNs with the relation in the method for comparing any two IVIFNs based on a score function and three types of entropy functions is a complete chain and obtain that this relation is an admissible order. Moreover, we demonstrate that IVIFNs are complete chains to the relation in the comparison method for IVIFNs on the basis of score, accuracy, membership uncertainty index, and hesitation uncertainty index functions.

Generative models which use explicit density modeling (e.g., variational autoencoders, flow-based generative models) involve finding a mapping from a known distribution, e.g. Gaussian, to the unknown input distribution. This often requires searching over a class of non-linear functions (e.g., representable by a deep neural network). While effective in practice, the associated runtime/memory costs can increase rapidly, usually as a function of the performance desired in an application. We propose a much cheaper (and simpler) strategy to estimate this mapping based on adapting known results in kernel transfer operators. We show that our formulation enables highly efficient distribution approximation and sampling, and offers surprisingly good empirical performance that compares favorably with powerful baselines, but with significant runtime savings. We show that the algorithm also performs well in small sample size settings (in brain imaging).

Probabilistic circuits (PCs) are a family of generative models which allows for the computation of exact likelihoods and marginals of its probability distributions. PCs are both expressive and tractable, and serve as popular choices for discrete density estimation tasks. However, large PCs are susceptible to overfitting, and only a few regularization strategies (e.g., dropout, weight-decay) have been explored. We propose HyperSPNs: a new paradigm of generating the mixture weights of large PCs using a small-scale neural network. Our framework can be viewed as a soft weight-sharing strategy, which combines the greater expressiveness of large models with the better generalization and memory-footprint properties of small models. We show the merits of our regularization strategy on two state-of-the-art PC families introduced in recent literature -- RAT-SPNs and EiNETs -- and demonstrate generalization improvements in both models on a suite of density estimation benchmarks in both discrete and continuous domains.

An outlier is an event or observation that is defined as an unusual activity, intrusion, or a suspicious data point that lies at an irregular distance from a population. The definition of an outlier event, however, is subjective and depends on the application and the domain (Energy, Health, Wireless Network, etc.). It is important to detect outlier events as carefully as possible to avoid infrastructure failures because anomalous events can cause minor to severe damage to infrastructure. For instance, an attack on a cyber-physical system such as a microgrid may initiate voltage or frequency instability, thereby damaging a smart inverter which involves very expensive repairing. Unusual activities in microgrids can be mechanical faults, behavior changes in the system, human or instrument errors or a malicious attack. Accordingly, and due to its variability, Outlier Detection (OD) is an ever-growing research field. In this chapter, we discuss the progress of OD methods using AI techniques. For that, the fundamental concepts of each OD model are introduced via multiple categories. Broad range of OD methods are categorized into six major categories: Statistical-based, Distance-based, Density-based, Clustering-based, Learning-based, and Ensemble methods. For every category, we discuss recent state-of-the-art approaches, their application areas, and performances. After that, a brief discussion regarding the advantages, disadvantages, and challenges of each technique is provided with recommendations on future research directions. This survey aims to guide the reader to better understand recent progress of OD methods for the assurance of AI.

Owing to the benefits for customers (lower prices), drivers (higher revenues), aggregation companies (higher revenues) and the environment (fewer vehicles), on-demand ride pooling (e.g., Uber pool, Grab Share) has become quite popular. The significant computational complexity of matching vehicles to combinations of requests has meant that traditional ride pooling approaches are myopic in that they do not consider the impact of current matches on future value for vehicles/drivers. Recently, Neural Approximate Dynamic Programming (NeurADP) has employed value decomposition with Approximate Dynamic Programming (ADP) to outperform leading approaches by considering the impact of an individual agent's (vehicle) chosen actions on the future value of that agent. However, in order to ensure scalability and facilitate city-scale ride pooling, NeurADP completely ignores the impact of other agents actions on individual agent/vehicle value. As demonstrated in our experimental results, ignoring the impact of other agents actions on individual value can have a significant impact on the overall performance when there is increased competition among vehicles for demand. Our key contribution is a novel mechanism based on computing conditional expectations through joint conditional probabilities for capturing dependencies on other agents actions without increasing the complexity of training or decision making. We show that our new approach, Conditional Expectation based Value Decomposition (CEVD) outperforms NeurADP by up to 9.76% in terms of overall requests served, which is a significant improvement on a city wide benchmark taxi dataset.

Google is paying tribute Tuesday to the computer scientist who created the mathematical framework "fuzzy logic." On this day in 1964, Zadeh submitted the paper "Fuzzy Sets," which laid out the concept of "fuzzy logic." The logo featured on Google.com "The theory he presented offered an alternative to the rigid'black and white' parameters of traditional logic and instead allowed for more ambiguous or'fuzzy' boundaries that more closely mimic the way humans see the world," reads a biography of Zadeh by Google. The theory has been used in various tech applications, including anti-skid algorithms for cars.

Power curves capture the relationship between wind speed and output power for a specific wind turbine. Accurate regression models of this function prove useful in monitoring, maintenance, design, and planning. In practice, however, the measurements do not always correspond to the ideal curve: power curtailments will appear as (additional) functional components. Such multivalued relationships cannot be modelled by conventional regression, and the associated data are usually removed during pre-processing. The current work suggests an alternative method to infer multivalued relationships in curtailed power data. Using a population-based approach, an overlapping mixture of probabilistic regression models is applied to signals recorded from turbines within an operational wind farm. The model is shown to provide an accurate representation of practical power data across the population.